# The position of a moving particle at time t is $\stackrel{\to }{\mathrm{r}}=3\stackrel{^}{\mathrm{i}}+4{\mathrm{t}}^{2}\stackrel{^}{\mathrm{j}}-{\mathrm{t}}^{3}\stackrel{^}{\mathrm{k}}$. Its displacement during the time interval t = 1 sec to t = 3 sec will be 1. $\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{k}}$ 2. $3\stackrel{^}{\mathrm{i}}-4\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{k}}$ 3. $9\stackrel{^}{\mathrm{i}}+36\stackrel{^}{\mathrm{j}}-27\stackrel{^}{\mathrm{k}}$ 4. $32\stackrel{^}{\mathrm{j}}-26\stackrel{^}{\mathrm{k}}$

Subtopic:  Position & Displacement |
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A cat is situated at point A (0, 3, 4) and a rat is situated at point B (5, 3, $-8$). The cat is free to move but the rat is always at rest. The minimum distance traveled by the cat to catch the rat is:

1. 5 unit

2. 12 unit

3. 13 unit

4. 17 unit

Subtopic:  Position & Displacement |
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Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance of 120 m. Which of the following statements is correct?

1. The balls can never meet.

2. The balls can meet if the ball B is thrown 1 s later.

3. The two balls meet at a height of 45 m.

4. None of the above

Subtopic:  Relative Motion |
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A body is projected at an angle of $30°$ with the horizontal with a speed of 30 m/s. What is the angle made by the velocity vector with the horizontal after 1.5 sec? (g = 10$\mathrm{m}/{\mathrm{s}}^{2}$)

1. $0°$

2. $30°$

3. $60°$

4. $90°$

Subtopic:  Projectile Motion |
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A particle moves along the positive branch of the curve y = $\frac{{\mathrm{x}}^{2}}{2}$ where x = $\frac{{\mathrm{t}}^{2}}{2}$, & x and y are measured in metres and in seconds respectively. At = 2s, the velocity of the particle will be

1.

2.

3.

4.

Subtopic:  Speed & Velocity |
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A deer wants to save her life from a lion. The lion follows a path whose equation is ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}=16$. For saving her life, the deer needs to move on a path whose equation will be

1. ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}=4$

2. ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}=16$

3. ${\mathrm{x}}^{2}+{\mathrm{y}}^{2}-64=0$

4. Both (1)and(3) are correct

Subtopic:  Circular Motion |
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A particle rotates in a circular path starting from rest. If angular acceleration is 4 $rad/{s}^{2}$, then the time after which angle between net acceleration and tangential acceleration becomes $45° is$

1. 0.5 s

2. 0.25 s

3. 2 s

4. 4 s

Subtopic:  Circular Motion |
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An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at x = –2m, its velocity is –(4 m/s)$\stackrel{^}{\mathrm{j}}$. What is the object's acceleration when it is at y = 2m?

1.

2.

3.

4.

Subtopic:  Circular Motion |
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To the captain of a ship A travelling with velocity $\stackrel{\to }{{v}_{A}}=\left(3\stackrel{^}{i}-4\stackrel{^}{j}\right)$ km/h, a second ship B appears to have a velocity ${\stackrel{\to }{v}}_{B}=\left(5\stackrel{^}{i}+12\stackrel{^}{j}\right)$ km/h. What is the true velocity of the ship B?

1.

2.

3.

4. none of these

Subtopic:  Relative Motion |
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A particle has an initial velocity $\stackrel{\to }{\mathrm{u}}=\left(4\stackrel{^}{i}-5\stackrel{^}{j}\right)$ m/s and it is moving with an acceleration $\stackrel{\to }{\mathrm{a}}=\left(\frac{1}{4}\stackrel{^}{i}+\frac{1}{5}\stackrel{^}{j}\right)m/{s}^{2}$. Velocity of the particle at t =2s will be

1. $\left(6\stackrel{^}{\mathrm{i}}-4\stackrel{^}{\mathrm{j}}\right)\mathrm{m}/\mathrm{s}$

2. $\left(4.5\stackrel{^}{i}-4.5\stackrel{^}{\mathrm{j}}\right)\mathrm{m}/\mathrm{s}$

3. $\left(4.5\stackrel{^}{i}-4.6\stackrel{^}{\mathrm{j}}\right)\mathrm{m}/\mathrm{s}$

4. $\left(6\stackrel{^}{\mathrm{i}}-4.6\stackrel{^}{\mathrm{j}}\right)\mathrm{m}/\mathrm{s}$

Subtopic:  Uniformly Accelerated Motion |
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